Question: Simplify the following expression: $r = \dfrac{7z}{4} + \dfrac{5z}{2}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $4$ and $2$ $\lcm(4, 2) = 4$ $ r = \dfrac{1}{1} \cdot \dfrac{7z}{4} + \dfrac{2}{2} \cdot \dfrac{5z}{2} $ $r = \dfrac{7z}{4} + \dfrac{10z}{4}$ $r = \dfrac{7z +10z}{4}$ $r = \dfrac{17z}{4}$